Re: Integration

[Sumaia Saad-Eddin <saadeddi@math.univ-lille1.fr>]

Le lundi 11 octobre 2010 Ã 14:54 +0200, Sumaia Saad-Eddin a Ãcrit :
> Dear all,
> 
>   here is a simple script I use:
> ----------------------------------------------------
> {calF3b(n, y, borne=0)=
>    local(res);
>    if(borne == 0,
>       res = intnum(u = y, [[1], I], 
> 		   (n*(n-1)*log(u/y)^(n-2)
> 		    -n*log(u/y)^(n-1)
> 		    +2*(-n*log(u/y)^(n-1)+log(u/y)^n))*(-cos(u))/u^3
> 		  )*2/factorial(n),
>       res = intnum(u = y, borne, 
> 		   (n*(n-1)*log(u/y)^(n-2)
> 		    -n*log(u/y)^(n-1)
> 		    +2*(-n*log(u/y)^(n-1)+log(u/y)^n))*(-cos(u))/u^3
> 		  )*2/factorial(n));
>    return(res);
> }
> -------------------------------------------------
> And then:
> ------------------------------------------------
> ? default(realprecision, 200);
> ? calF3b(3, 5, 0)
> %24 =
> -0.0014856416479696953928448903497326047373162140908013809557457050551373320878332013935070207158553203686531222066372995251233206569487841668099460986174588469189370065932422491349757424944029721562740578
> ? calF3b(3, 5, 1000)
> %25 =
> -0.0014856627355888837790517373518799598562592890176944537692015849210748454162194856065031296971028332780195925404567414258318215629128028619431494341708703232462104962505815455183302302207438155760827252
> ? calF3b(3, 5, 10000)
> %26 =
> -0.0014797277179347064177532972573409986024162997470900911555361077225939621992399038808681398516168186547356007049683292650261103144255778980107135555010306584599354594552108552028831561946152770233217702
> ? calF3b(3, 5, 100000)
> %27 =
> -0.0014923749632841228130828117074689824573212046115472117963604716758907190884104283414505365906272331638082132284475597672118202238948186809803203022515326726288826288931730256153115499066993338887350605
> ----------------------------------------------
> 
> Can anyone explain me why these results are so 
> different, or give me a pointer to some litterature?
> Many thanks in advance!
> Sumaia